It's called an offer, or proposal. If the $400 is in effect "illusory," you are on shaky legal ground, however.
In legal terms, a contract consists of six parts: 1) an offer; 2) an acceptance; 3) consideration; 4) legality; 5) contractual capacity; and 6) contractual intent. If any ONE of the preceding parts is missing, there is no legal contract.
First, an offer: For there to be an offer, there must be a clear and unambiguous communication of a sincere intention on the part of one person to enter into an agreement with another person.
Does your offer to your customer represent a sincere intention on your part to sell a car to him for $400? If so, you just made him an offer. YOU are the offeror.
Second, the acceptance: The ball is now in your customer's court, and he calls the shots. He is the offeree. If he says "yes," you are on your way to forming a legal contract; if he says "no" and makes you a counteroffer, the ball is then in your court; you can accept or reject his counteroffer and perhaps counter his counteroffer, and so on, until you've reached a mutually-agreed-upon price.
I find it hard to believe a "magnificent car" can be purchased for a mere "$400, but it is not unheard of, I suppose.
Third is the consideration: It's the old "value for value, quid pro quo" step in forging an agreement. The "subject" of the deal is exchanged for something else; in this case a car for money, though the consideration need not be money; it could be virtually anything of value.
These first three elements of a legitimate contract are the three most important of the six because they form the provisions of the contract itself; without them, there is no contract.
Fourth is contractual capacity. If the offeree is of legal age (18 in some states, 21 in other states) AND has the mental ability to enter volitionally and rationally into a contract, then capacity exists.
If the offeree is either not of age or incapable due to mental defect to enter into a contract, then the contract, once consummated, is voidable. That is, if the offeree or, say, his parent, wants to nix the deal, then he may do so and the things of value that were exchanged must be returned to each party.
Fifth, there is legality. If in consummating the deal, one party is breaking the law in some way, the contract is void. Period.
A "contract" to kill a person will always be void and malum in se (considered wrong, inherently and universally), as will a "contract" between a "John" and a prostitute (except in maybe two counties in the state of Nevada--and one of them is NOT Las Vegas!), which is malum prohibitum (wrong by law or statute). And
Sixth, there must be contractual intent, and the intent must be legitimate.
If there is an element of coercion, duress, undue influence, deception, or downright fraud, there can be no valid contract. Period. When a salesperson tries to sell you a car cheaply because he knows the car is a piece of crap and will likely break down five miles after it is driven off the used-car lot, an element of fraud exists, particularly if he offers you a thousand-mile warranty but has no intention of honoring that warranty.
It is said, "Let the buyer beware"; it is also said "Let the seller beware." There must be legitimate contractual intent on both sides. If the offeree puts a gun to the offeror's head and says, "Sell me this car for a hundred bucks, or I'll blow your brains out," that contract is voidable and is not really a contract at all, because of the element of duress.
Who wants to get shot over a hundred bucks? Not I! I'd sign that contract in a heartbeat. Later, though, I'd involve the cops in the affair and insist the car be returned, and I in turn would give the money back to the "offeree" as the police cart him off to jail.